Introduction

In a post-truth period in which the very nature of facts has been called into question -- challenged as they are by alternative facts -- there is a case for exploring this condition by every means possible. Clearly there are implications for both global governance and how individuals can now best navigate daily life and its opportunities -- whether they prefer to indulge in the reality of "facts" or the surreality of "imagination".

The exercise interrelates implications from several disparate frameworks -- deliberately exploiting poetic licence and metaphor. It was inspired by the manner in which "alternative facts" can readily be defined as "bull" in popular jargon -- or even more explicitly, as distinctively clarified by the philosopher Harry Frankfurt (On Bullshit, 2005; On Truth, 2006). This had evoked the need to derive new insights from "bullfighting", metaphorically understood (Viable Global Governance through Bullfighting: challenge of transcendence, 2009).

Any response to "bull" also calls for recognition of the centuries of insight derived from the successive phases in the evolution of insight, as frequently depicted in Zen Buddhism by a traditional set of Ten Bulls. Rather than as a "bull", of potential relevance is the extent to which the animal is ambiguously identified as an "ox" -- through a set of 10 "ox-herding" pictures, each with a brief commentary (cf D. T. Suzuki; Kubota Ji'un, Ten Ox-herding Pictures with the Verses Composed by Kakuan Zenji, 1996).

The bull/ox ambiguity offers an interesting implication for the manner in which the dangers of the bull in the chaotic reality of the wild may be tamed and domesticated through a cognitive form of "castration" ("emasculation") -- as with other truths of reality held to be dangerous. The threat of any such animal also recalls the famous comment by John Maynard Keynes regarding the challenge of "animal spirits". As noted, for example, by Robert Shiller (Animal Spirits Depend on Trust, Wall Street Journal, 27 January 2009; George A. Akerlof and Robert J. Shiller, Animal Spirits: how human psychology drives the economy, and why it matters for global capitalism, 2008).

There is then of course the paradox as to the appropriateness of dealing with chaotic wildness forms of "domestication", recalling the argument of Aldous Huxley:

To make biological survival possible, Mind at Large has to be funneled through the reducing valve of the brain and nervous system. What comes out at the other end is a measly trickle of the kind of consciousness which will help us to stay alive on the surface of this particular planet... Most people, most of the time, know only what comes through the reducing valve and is consecrated as genuinely real by the local language. (The Doors of Perception, 1954)

Donald Trump is now upheld as an exemplar of chaos, perhaps to be recognized as corresponding to the trickster archetype (Coyote, Loki, etc), as discussed separately (Identity in question via Trump: Narcissus vs Loki? 2016). The question here is whether the stages and possibilities of individual or collective insight (into the nature of facts and evidence) can be fruitfully reframed in relation to imaginative engagements with the surreal and with "bull" -- as an effective strategic response.

The surreal could be characterized by the many mutually contradictory declarations of politics, religions and the sciences, with their "creative" approaches to concrete proof in which people are insistingly called upon to believe. These are echoed by insights into the social construction of reality, and more especially through use of "fiat", as with the fiat money now characterized by previously deprecated quantitative easing.

In implying degrees of self-reference here, the use below of the 10-bull framework, is further elaborated by the device of recursively embedding the cognitive challenges of each into each. Each of the 10 phases then constrains and colours understandings of the other 10 phases within that embedding -- making a potential set of 100 distinctions. However, rather than a linear sequence of "stages", of greater potential relevance are the dynamics between their emergence and co-existence in practice -- and how these might be understood in the present rather than in the hypothetical future. Hence the use of "phases".

The pattern as a whole then offers a fruitful means of exploring the variety of possible understandings of "fact", "existence" and credible "proof", notably as addressed by the philosophical concerns with facticity. As might be expected, the latter has a multiplicity of meanings from "factuality" and "contingency" to the intractable conditions of human existence. The approach here is necessarily only suggestive and exploratory -- without any claim to definitive closure. Rather it could usefully evoke discussion as to whether the additional articulations are appropriately made or could be more meaningfully distributed otherwise.

The primary concern is how to engage with "bull" in this period, thereby calling into question the currently preferred use of fighting metaphors in response to Donald Trump, typical of "bull fighting" (Enhancing Sustainable Development Strategies through Avoidance of Military Metaphors, 1998). The ambiguity of "bull" in the Zen phases is succinctly indicative of the self-referential process of engaging with an emergent pattern of abstraction of greater subtlety -- both in terms of of its intractable dynamic and its deprecation as a delusion or conceit from any more conventional perspective.

Tentative correspondences within a 10-bull framework

Previous uses and possibilities: The following indicate possible adaptations from other perspectives:

experience of action engendering new consciousness: as articulated with extensive commentary on the first six images by Yong Zhi: wandering in wilderness ; discover the path ; focus on the object ; engage the object ; control the object ; harmonious interplay between subject and object (Human Actions illustrated in Zen's Ox-Herding Pictures, Humanities, 2012)

problem integration: Phases in the sequence of cognitive Integration of Perceived Problems (commentary with respect to the World Problems Project of the Encyclopedia of World Problems and Human Potential)

progression to higher orders of consensus, through which possibilities of integrating the shadow are embodied, as separately suggested in the context of the Global Strategies Project (Strategic denial: Reframing the unknown)

The existentialist Martin Heidegger, the psychologists Carl Jung and Erich Fromm, and the musician John Cage, all acknowledge Suzuki's influence on their work and thought. Correspondences with other patterns of spiritual insight have been noted in the case of the Enneagram (João C. Fontes, Enneagram, Jesus and the Way, 2008) and the Kabbalah (Marek Bazgrzacki, The Cabalah, Philosophy and Buddhism, 2011).

The concern here is to distinguish a set of functional correspondences with respect to each such stage. This is necessarily extremely tentative. The elaboration of such a set can of course be explored through the question of the number of such functions that can be distinguished -- especially when the number is constrained to ten. The set could of course be refined in the light of insights from a range of disciplines. The value of the Zen set is its appreciated coherence over centuries.

These are typically associated with the models proposed by particular schools of thought, notably those deriving from Jean Piaget and Carl Jung. The systemic coherence of a restricted set of functions distinguished may give rise to particular patterns (possibly non-linear), as with the AQAL pattern of Ken Wilber, the Myers-Briggs Type Indicator, the Team Role Inventory of Meredith Belbin, the enneagram of personality, and the like. It is unclear how well adapted these are to any engagement with the surreal nature of a post-truth era.

To be free of the illusory nature of "ontological dualism", however, one must journey through stages of increasing awareness, admirably depicted in the ten illustrations of the "Oxherding Pictures". From seeking a self (ox) that one thinks one has lost, to glimpsing the self that is first elusive and finally illusory, the seeker comes to realize that all identities are constructed and therefore temporary, including such notions as "race" and "self". (Richard Collins. Honoring the Form: Zen Moves in Charles Johnson's Oxherding Tale. Religion and the Arts, 14, 2010)

As a mnemonic catalyst, "bull" can be variously understood in the light of the following "stories" which might be framed in terms of a 10-bull context.

engagement with a goal or target ("bull's eye"): with distinctions notably made by the philosopher Eugen Herrigel in the much-cited Zen in the Art of Archery (1948), which has been an inspiration for some 200 goal-oriented studies with similar titles

degrees of model comprehensiveness: towards a Theory of Everything, a hypothetical all-encompassing philosophical explanation of nature or reality; notably as a framework provided by Ken Wilber in explaining his "ntegral theory" (A Theory of Everything, 2001)

degrees of martial arts skill: as implied by the set of 10 dan ranks (with some correspondence to rankings in the board games of go and shogi). Exemplified in use of the ox-herding images to discuss the spiritual and ethical dimensions of martial arts training (John J. Donohue, Herding the Ox, 1998)

degrees of illusion: understood as cognitive biases, an extensive range of these have been organized into four categories: biases that arise from too much information, not enough meaning, the need to act quickly, and the limits of memory (John Manoogian III, Cognitive Bias Codex). Such organization can be contrasted with the degrees of illusion highlighted in relation to Maya by Hinduism and Buddhism.

degrees of credibility of claims: there are degrees of credibility and incredibility (as noted by the Credibility Weekly) whether with respect to claims or sources, posing obvious issues of communication. In science credibility is framed in terms of degrees of correlation measured by a variety of coefficients with the consequent implication of degrees of belief in any model (Wen Jiang, A correlation coefficient of belief functions, 2016).

Common titles of the ox-herding pictures in English, and common themes of the associated prose, are indicated in the second and third columns. Given the concern with collective implications, in addition to the traditional individual preoccupation, clusters of synonyms are presented below to clarify interpretation of the function tentatively named in the fourth column.

externally observed objects are modcllcd with an observer's noumenal view and voice that is systematically excluded from the "objective" model of the world to create the effect that the ''true natural world" in-itself is looking and speaking at the subject [eg science]

observer's noumenal view and voice of externally observed objects is included in the model thus creatively relativizing thc observer's "objective" world model to the subjective locus producing it in order to study its effects in the ideational field structuring the motion of subject-object [eg deconstruction]

observer of externally observed objects reflectively incorporates its own and subjective-multiplicities as a (virtual, extimate) object of analysis structured by an a priori frame of desire that unconsciously filters orientation, intervention, and understanding of subject-object entanglement [eg psychoanalysis]

observer identifies the virtual ideational field composed of a multiplicity of self-relating and desiring world views and voice models as a universal agency ("scmiospherc'') in-itself with asymmetrical and irreversible reflective and creative autonomy structuring the motion of subject-object entanglement [eg history itself]

The construction of a reliable index of bullshit receptivity is an important first step toward gaining a better understanding of the underlying cognitive and social mechanisms that determine if and when bullshit is detected. Our bullshit receptivity scale was associated with a relatively wide range of important psychological factors. This is a valuable first step toward gaining a better understanding of the psychology of bullshit.

The Zen images are appreciated in that tradition because they avoid "verbose" articulations of a variety of coherent conditions of experience. Other verbal articulations could of course be matched with that set of images, notably levels of meta-distinction and abstraction in physics and metalogic. All such distinctions could be explored in terms of levels of dialogue (Varieties of Dialogue Arenas and Styles, 1997). It could be understood in terms of the phases of any hero's journey as distinguished by Joseph Campbell in terms of 17 stages (The Hero with a Thousand Faces, 1949). Such myths do not necessarily contain all 17 stages explicitly; some myths may focus on only one of the stages, while others may deal with the stages in a somewhat different order.

Perhaps more intriguing, the challenge could be framed by mixing musical and chemical metaphors (Tuning a Periodic Table of Religions, Epistemologies and Spirituality, 2007). There is a sense in which each column in such a table (termed a group) could be associated with the cognitive implications of a Zen "bull", progressing successively along the row towards a form of completion. The rows of the table then offer a means of holding subtler (and rarer) implications. The complexities of the table with respect to 8 or more groups, could then frame reflection on the complexities of "bull" (as discussed further below).

The preliminary attribution of text to the sub-phases of the following 10 phases is necessarily both highly tentative and far from adequate -- as evident from minimal or absent text in many cases. Extensive use of "bull" is employed as an indicative code for a complex of possible associations.

Implication in interwoven "bull" and "ox" themes

The images used in the animations below have been slightly adapted from those in the Wikipedia entry on Ten Bulls by Tensho Shubun (1444). That entry also offers the contrasting images of Ten Bulls by Tokuriki Tomikichiro (1902-99).

Seemingly the most general sense of "bull" is associated with recognition of an unusual emergence, disrupting the anticipated flow of things. Thus a Wikipedia entry on the disambiguation of bull notes its use for decrees (whether the imperial Golden bull, or the Papal bull), with bulletin now having a similar etymological derivation. The use of tweets by Donald Trump might be seen as combining both the sense of decree and bulletin, as well as their deprecation as "bull". The term is also used in the financial markets as a particular form of stock market speculation (with its associated bull market).

Especially intriguing is the complex of associations evident in the etymology of "bullet" (as some form of projectile), a diminutive deriving from the roundness of a ball -- especially a cannon ball. Noteworthy is its use in bullet points in the "projection" of the points in a presentation. A bullet loan is a mode of payment of a debt instrument (with which a balloon payment may be associated). The capacity to bite the bullet is understood to involve accepting the negative aspect of a situation and engaging realistically with it, whereas dodging a bullet is the avoidance of any such disaster. Astronomy distinguishes newly merging galaxies as a bullet group.

The semantic field is rendered more complex by inclusion of bullying, with ambiguities to its own etymology -- associated to some degree with "bull". The intimidation can be recognized in a complementary process, namely the blood sport of bull-baiting. Given the manner in which people can be verbally bullied, of further interest is use of bully pulpit as a conspicuous position that provides an opportunity to speak out and be listened to. Extensive use of Twitter by Donald Trump could be understood in such terms.

In this period, with the increasing recourse to use of "bull", bullets and explosive "self-projection" in reaction to negligent indifference (and spurious argument), such complementary associations could offer a key to greater comprehension of the disruptive recourse to violence (Global Incomprehension of Increasing Violence, 2016). As a source of disruption, especially intriguing is the lack of focus on the source of "bull" in its various forms, exemplified in the case of projectiles (Identification of Bullets: human right and human responsibility? 2009).

significance of the absent "cow", despite its importance in mythology; cow vs bull/ox; "cow" as a current deprecation of female (further exemplified by "sacred cow")

"cowshit" vs "bullshit" (as variously debated, most notably with respect to political correctness, and the obvious lack of any indication of "human shit")

the form taken by the spirit of the bull, after its vehicle has been transformed into an ox

the radical cognitive shift associated with the much-cited assertion to students that Buddha is a shit stick (Zen master Yunmen), inspiring recent references to the "shitting Buddha", and appropriated as the title of a digital album.by Tom Spademan. No other religion reframes blasphemy in this way. As indicated by Joseph Grcic:

This is often interpreted to mean that the teachings of the Buddha are to be used as a means ro enlightenmenc and then to be discarded, not to worship Buddha or his teachings as necessarily the absolute truth. The same idea is conveyed in the following question: What should you do when you meet the Buddha on the road? Answer: Kill him. That is, we should eventually be independent of the Buddha and all authorities and ideologies and think for ourselves. (Facing Reality: an introduction to philosophy, 2009, p. 208)

The set of themes above suggests the possibility that further significance might be derived from ordering them in some manner -- possibly consistent with the Zen pattern.

Facticity, alternative facts and Zen?

Facticity is defined to be the condition or quality of being a fact.

Existentialism: As noted above, in philosophy, facticity has however a multiplicity of meanings from "factuality" and "contingency" to the intractable conditions of human existence. Any discussion of it is immediately embroiled in the subtle obscurities of phenomenology and existentialism, notably as framed by Martin Heidegger (Ontology: the hermeneutics of facticity, 2008) and Edmund Husserl (N. Depraz and D. Zahavi, Alterity and Facticity: new perspectives on Husserl, 1998). As noted by the Stanford Encyclopedia of Philosophy with respect to Facticity and Transcendence:

Human existence, then, cannot be thought through categories appropriate to things: substance, event, process. There is something of an internal distinction in existence that undermines such attempts, a distinction that existential philosophers try to capture in the categories of "facticity" and "transcendence". To be is to co-ordinate these opposed moments in some way, and who I am, my essence, is nothing but my manner of co-ordinating them. In this sense human beings make themselves in situation: what I am cannot be separated from what I take myself to be...

Facticity includes all those properties that third-person investigation can establish about me: natural properties such as weight, height, and skin color; social facts such as race, class, and nationality; psychological properties such as my web of belief, desires, and character traits; historical facts such as my past actions, my family background, and my broader historical milieu; and so on. I am not originally aware of my facticity in this third-person way; rather, it is manifest in my moods as a kind of burden, the weight of "having to be". However, I can adopt a third-person or objectifying stance toward my own being, and then these aspects of my facticity may appear precisely as that which defines or determines who I am.

In that context, facticity is a continuing focus of debate (François Raffoul and Eric Sean Nelson (Eds.). Rethinking Facticity, 2009). This has notably been extended to current political issues (Michael J. Shapiro, Deforming American Political Thought: ethnicity, facticity, and genre, 2006; Georgia Triolo, Antigone Unmasked: fate/facticity/genetic fallability, 2010).

With respect to the international community, Noam Chomsky has noted its use as referring to the United States and its client states and allies, most notably in the media of those countries:

The literal sense is reasonably clear; the U.N. General Assembly, or a substantial majority of it, is a fair approximation. But the term is regularly used in a technical sense to describe the United States joined by some allies and clients. (Henceforth, I will use the term "Intcom", in this technical sense.) Accordingly it is a logical impossibility for the United States to defy the international community (The Crimes of 'Intcom', Foreign Policy, September, 2002)

Subsequently Chomsky is quoted as stating:

Where the term (international community) is used in the West, the international community refers to the United States and anyone who happens to be going along with it. If the world happens to be, most of the world is opposed, they're just not part of the international community (Israel, US violators of international law, The News Tribe, 14 June 2012).

Clearly such questions have implications for how individuals can be held to exist -- or be experienced as existing, whether by others or by themselves --- yesterday, today and tomorrow.

Facticity and alternative facts: The considerations above have obvious implications for the manner in which some humans are (or have been) framed as "nobodies", "subhuman", and/or "without souls". Such assessments, formally made, can be upheld as "facts" -- often with fatal consequences, as evident following the authoritative religious justification for genocidal massacre of indigenous peoples by colonial powers. Instances in other domains include:

religion: The fatal interplay between the Abrahamic religions over centuries could be framed in terms of assertions of fact by each (in the light of the unquestionable Word of God embodied in their respective scriptures) and the condemnation as anathema of the alternative facts (promoted as fact) by their religious peers and siblings. Their tragedy, irrespective of the cost, is the complete inability to explore matters otherwise -- and a total lack of motivation to do so (Systemic Reliance of World Religions on Human Sacrifice, 2014). However it is possible that history will describe the fundamental constraint of science as having had its "nose pressed too firmly pressed against the window" of facticity, just as religion has had its "nose pressed too firmly against the window" of its obverse.

figures of speech: More intriguing is the case of widely appreciated imaginative figurative expression, as in poetry, fantasy, story-telling, or through the use of metaphor. This extends to the use of humour in reframing a situation. Are these the acceptable face of "alternative facts"? Poetry and humour are as irrelevant to the theories of science as they are to the arguments of theology. (Questionable Classification of Figures of Speech, 2016).

myths and legends-- stories: More problematic is the case of myths and legends in which people variously believe and celebrate -- as might include the predictions of astrology? As "superstition", are these alternative facts a "superposition" on factual reality -- an adulteration of it to be systematically deplored?

terrorism: Currently of the greatest relevance is any assertion, as a "fact", that an individual is a terrorist -- when for some they may be upheld as freedom fighters, as history may uphold them to be. The heroic figures of many cultures and nations may well have been labelled terrorists, or would be claimed to be so by current criteria: George Washington, Nelson Mandela, Jomo Kenyatta, Menachem Begin, etc. At the time of writing the paradox is remarkably indicated by the case of Martin McGuinness (McGuinness 'was a freedom fighter, not a terrorist', BBC News, 24 March 2017; What Martin McGuinness's eulogisers would like to forget, The Spectator, 25 March 2017). Which heroic national icons have not been so labelled? On the other hand many who engender terror are not framed as "terrorists", as in the case of bullies, racketeers, and the like -- as well as others who engage in intimidation through their positions of power in institutions (as with some employers, priests, and military superiors).

contradictions: Such considerations raise the question as to whether "contradictions" constitute a more formal recognition of "alternative facts". The issue is most obvious in the case of unquestionable assertions of experts -- possibly qualified as being "professional opinions". Subtler variants could be understood in this light.

conspiracy:
As noted by Paul Ratner: Once a conspiracy theory becomes the accepted explanation, it stops being a conspiracy theory and becomes a fact of history. This certainly is one reason people continue to believe -- they hope their views will eventually be proven right (America's 10 Most Popular Conspiracy TheoriesBig Think, 19 March 2017).

advertising, image management: As in the widespread use of hyperbole and superlatives in claims made. Irrespective of any cultivation of misunderstanding, misrepresentation is supposedly avoided through the technical legitimacy of puffery. The issue relates to negative campaigning, scandal-mongering and "fake news". It is well-framed by the widely cited remark of Howard Hughes: Never check an interesting fact.

deception and disinformation: These are considered vital to the process of engagement with any opponent. Slender facts are smothered with weighty assumptions and upon which are woven a hefty garment of allegations, speculation and imagination fitting with the occupational predisposition to detect a spy (Ray McGovern, Another Hatchet Job on Snowden, Information Clearing House, 5 March 2017). Similarly bluff and sleight of hand are variously accepted as a necessary skill in strategic undertakings, irrespective of any interpretation as confidence trickery

disagreement in debate: Especially interesting is the possibility that disagreement in debate on many major strategic issues is characterized by the interplay of assertions of fact and alternative interpretations of their facticity, as evidenced by denial of climate change, environmental degradation, or overpopulation. Is the debating process an exploration of facticity -- particularly when themes are considered irrelevant to any consideration in that context.

Let's begin with Arendt's comment that truth is neither given to nor disclosed to but produced by the human mind. If "truth" is not "given," then we must understand that it is constructed and contextual, which means that even as it asserts its "facticity," it is not beyond interrogation. Let's consider this in the light of the Student Learning Goals adopted at Oberlin in 2015. The first goal, deepening understanding in specific fields, recognizes that A deeper understanding of a specific field of study generates the potential for students to move beyond the skills of analyzing and evaluating information and towards the creation of new knowledge or approaches, or the production of original work.

The issue framed by the Zen pattern would seem to be in the nature of that "deeper understanding". To what extent is a logical fallacy to be considered a fact when challenged by the potentially paradoxical nature of any deeper understanding -- if only in fundamental physics?

As the close etymological connection between terms such as facticity and factitiousness suggests, it is not easy to finely separate the factual from the fake. False concretions can be used to deny much more complex facts: a snowball "disproves" global warming, a sinister conspiracy distracts from systemic issues. As fake news and "alternative facts" triumph, the complexity of facticity is denied. However, ritualistic "fact checking" is in itself not a solution as the performativity of social media goes into overdrive. What is the potential of aesthetic and artifactual practices in this situation? (Institute of Contemporary Art, Miami, 30 March 2017)

Although definitions vary, cultural relativism is characterized by a reluctance to take one culture's norms as authoritative, not only because there may be no such standard (the postmodern position), but also, and perhaps more importantly, because asserting such normative authority demeans other cultures. It's not that objective facts don't exist -- it's that asserting their existence is rude, oppressive, biased. The primary justification of relativism shifts from epistemology to ethics.... The notion of "truth as disrespect" powers the current assault on facts. Trump and much of his base reject the truth-making mechanisms of academic culture by appealing to anti-elitism, and sow uncertainty via indignation and cultural pride. Why should pompous experts get the last word on the truth when working-class folk have their own ideas about it? .... Tribal epistemology has met with severe resistance from journalists, who have shifted away from a hands-off approach to truth and started reporting explicitly on the facticity (or lack thereof) of claims.

It would seem that, at least for some, facticity is in no way an unquestionable indicator of truth and that facticity may be a matter of degree intimately related to belief and credibility through complex subtleties that each may be challenged to comprehend -- as implied by the process of engagement in the Zen ox-herding pattern. Creativity and inspiration may well require a denial of conventional facticity. Identity may be especially associated with any particular sense of facticity.

The "taming" central to the sequence of Zen patterns merits consideration in the light of a reflection in his final years by Albert Einstein: Every true theorist is a kind of tamed metaphysicist. (Maria Popova, In Praise of the Tamed Metaphysicist: Einstein on reality, rationality, and the human passion for comprehension, Brain Pickings, 12 May 2016). This implies that the spirit of the bull is otherwise evident in the meta-perspective of the later images.

The question with respect to the USA is currently of great relevance in the light of the ongoing debate regarding the right to exist of Palestine -- recognized as it is by the vast majority of countries (John V. Whitbeck, The State of Palestine Exists, The Huffington Post, 1 September 2013). Given that debate, to what extent can the USA then be held to exist, or to have a right to exist? How could concrete proof be presented in support of that claim -- given such requirements with respect production of nuclear weapons by Iran, as discussed separately (10 Demands for Concrete Proof by We the Peoples of the World, 2012)?

Naming: Whilst a sense of existence invites naming, the process of naming can be deliberately used to determine existence and to appropriate what is so named. This recalls the psychosocial appropriation of a geopolitical space at the collective level described by the process of land nam, coined by Ananda Coomaraswamy (The Rg Veda as Land-Nama Bok, 1935), to refer to the Icelandic tradition of claiming ownership of uninhabited spaces through weaving together a metaphor of geography of place into a unique mythic story. This territorial appropriation process, notably practiced by the Navaho and the Vedic Aryans, was further described by Joseph Campbell (The Inner Reaches of Outer Space: metaphor as myth and religion, 2002):

Land nam ("land claiming or taking") was [the Norse] technical term for this way of sanctifying a region, converting it thereby into an at once psychologically and metaphysical Holy Land.... Land nam, mythologization, has been the universally practiced method to bring this intelligible kingdom to view in the mind's eye. The Promised Land, therefore, is any landscape recognized as mythologically transparent, and the method of acquisition of such territory is not by prosaic physical action, but poetically, by intelligence and the method of art; so that the human being should be dwelling in the two worlds simultaneously of the illuminated moon and the illuminating sun.

Possession of property: Of current relevance is the extent to which colonial powers have established and affirmed possession through renaming locations previously named by indigenous cultures. The pattern is now notable in countries like Ireland and New Zealand where English is presented in conjunction with the traditional names. A more complex situation exists in bilingual cultures where places have quite distinctive names in two or more languages, as in Belgium -- suggestive of their apprehension otherwise in each.

"Fiat reality"? As noted above, these issues are echoed by insights into the social construction of reality, and more especially through use of "fiat", as with fiat money and characterized by quantitative easing. More generally it could be argued that any current reference to "alternative facts" can be understood as a declaration reality -- a "fiat reality".

Facticity and belief: The two icons of cognitive science, Noam Chomsky and George Lakoff, continue to make unqualified assertions that Trump really lost the election -- clearly a belief to which they unquestionably subscribe. Is this tantamount to the elaboration of the kind of alternative fact of which Trump is so frequently mocked? Are human rights subject to misinterpretation in this way, as separately argued (Cultivating the Myth of Human Equality: ignoring complicity in the contradictions thereby engendered, 2016)?

Given calls for "concrete proof" with respect to nuclear programs in Iran, how are the "facts" formally announced to the UN Security Council in 2003 (regarding the existence of weapons of mass destruction in Iraq) to be compared with the "facts" justifying the missile attack in Syria in 2017? Will the inferences in both cases prove to have been equally unjustified?

Unsurprisingly the implications for understanding Donald Trump have been variously recognized -- complete with reference to the windfarms of Scotland (Navin J. Antony, Don, the quixotic, The Week, 20 November 2016; The Quixotic World of D. Trump,Trekking toward the Truth, 17 February 2017; Katy Waldman, Donald Quixote, Tilter at Wind Turbines, Slate, 22 December 2016). Should any uncritical model of reality be recognized as "tilting at windmills" -- at least to some degree?

Facticity might then be explored through the manner in which facts are created as a focus for belief (Barbara Hanson, The Research Process: creating facticity, 1999; Ragini Elizabeth Michaels, Facticity: a door to mental health and beyond, 1991). Of further relevance is any sense of degrees of facticity as implied separately (Towards articulation of a "post-truth table"? 2016)

Zen of facticity? Concern with facticity has been variously associated with Zen, but seemingly not with the 10-bull pattern. Thus for Thomas Merton (Mystics and Zen Masters, 1999):

The Zen insight is a direct grasp of being in itself, but not an intuition of the nature of being. Nor can the Zen insight be described in psychological terms, and to think of it as a subjective experience "attainable" by some kind of process of mental purification is to doom oneself to error and absurdity (p. 29)

Merton then comments on Kierkegaard's critique of Christianity as:

... [transferring] into the religious sphere all the facticity, the routine, and the falsity of "abstract levelling". Instead of obeying the Word and Spirit of God living and active in His Church, the body of those who love one another precisely insofar as they have been freed from facticity and routine, one surrenders at the same time one's human and one's religious integrity. (p. 272).

... historical and comparative analyses of Heidegger and Zen Buddhism are motivated by three simple ideas: 1) Zen is uncompromisingly non-metaphysical; 2) its discourse is poetic and non-rational; and 3) it aims to provoke a radical transformation in the individual, not to provide a theoretical proof or demonstration of theses about the mind and/or the world. To sketch this picture of Heidegger's thought, I draw on the two texts from his later work that command the most attention from commentator's seeking resonance with Zen, and discuss how his treatments of death, fallenness, facticity, and temporality in Being and Time square with Zen philosophy.

Of relevance to the Zen mode of depiction, Storey has subsequently argued that:

... Heidegger's desire to deconstruct the West implies the deconstruction of conventional views of learning because both aim to undercut the representational nature of thinking in order to recover thinking as a form of contemplation. Consequently, education should not be conceived as the acquisition of a more or less correct mental picture, but suggests the opposite: the relinquishing of all images in a contemplative aporia.(Heidegger East and West: philosophy as educative contemplation, Journal of Philosophy of Education, 2015)

Carl Olson notes that:

The Zen ideal is to act spontaneously in the situation without first objectifying it in order to define one's role (Zen and the Art of Postmodern Philosophy: two paths of liberation from the representational mode of thinking, 2000, p. 141)

In a discussion of Zen in relation to facticity, F. Schalow notes:

The worldly orientation of religious experience becomes explicit by allowing an ironic tone, a twist of contrariness, to impede the believer's normal expectations. The religious dimension thrives on this novel attunement, this medium of conveyance. Indeed, it is the echo of uncanniness in the familiar which lends credence to religious motifs. For example, the aloofness of God before the plight of humanity, as depicted in the Old Testament's story of Job, points to the radical asymmetry between human expectations and the inscrutable if not aloof character of the Divine. Job's self-revelation reminds us of our vulnerability before the unconquerable facticity of our lives; and Job's suffering offers a signpost to what is most unfathomable about God's relation to us, a clue to the radical otherness of that mystery. (Heidegger and the Quest for the Sacred: from thought to the sanctuary of faith, 2013, p. 88):

Schalow's reference to a "twist of contrariness" is usefully indicated by the early encounter with the back-end of the bull in the Zen pattern. The associated paradox can be recognized otherwise in terms of a cognitive twist, as discussed separately (Enantiodromia: cycling through the "cognitive twist", 2007).

Non-linear patterns of distinctions constrained by number

The concern in what follows is with challenges to comprehension and communication, especially as now exacerbated in a post-truth era. Anything can now be said and asserted to be "true" and a "fact". The Zen pattern suggests a means, framed by images, to indicate useful distinctions in navigating this reality.

Constraints and neglected functions: As noted above, the approach taken here is to explore the use of the Zen 10-fold pattern, given its acclaimed value in distinguishing degrees of insight -- consistent with degrees of self-reflexivity (Hilary Lawson, Reflexivity: the post-modern predicament, 1986). However a concern is how so many patterns of distinguished cognitive functions tend to identify only a limited number, conforming (suspiciously) to the much-cited insight of George Miller (The Magical Number Seven, Plus or Minus Two: some limits on our capacity for processing information, Psychological Review. 63, 1956).

In the tentative exercise above, it is of course the case that the distinctions made could be variously conflated, further articulated or ordered otherwise. If a 10-fold pattern of insight emergence is of value, there is of course the question of how Miller's cognitive constraint of "plus or minus two" relates to any pattern of "nine" or less, and of how a further "one" is excluded. What distinctive cognitive "functions" are most readily neglected (or conflated) in patterns of 5, 6, 7, 8 and 9?

Understood otherwise, it would appear that there is a poorly explored constraint highlighted by conventional representations of numbers. The sequence "starts again" having reached a limit, most commonly 10 (see List of numeral systems). This contrasts with any alphabet enabling "verbose" articulation considered acceptably adequate, most notably in academic, religious and political discourse. Images are typically avoided, especially when dissemination of texts is subject to the economic constraints of journal and book publishers.

Challenge to linear sequence: Many articulations of the development of insight emphasize a linear process. For example, as noted by The Oxford Handbook of Cognitive Literary Studies (2014):

Instead of using a "top-down" metaphor for such past-to-present processing, however, linguists and cognitive scientists might better speak of "back-to-front" processing. Both metaphors are spatial, but only the second captures the temporal signature of cognition, our compelling sense that time flows along a horizontal line and not up or down a vertical one. Based on our embodied, "forward-looking" or prospective orientation in space, the "back-to-front" metaphor likewise improves upon conventional conceptualizations of time as something that "goes by" or that we "get through". Where these conventional metaphors represent future time as standing before or coming toward us and past time as disappearing behind us, the "back-to-front" metaphor captures a salient fact about the direction of time in the actual process, as opposed to the conceptual products, of cognition. In cognition as distinguished from conceptualization, time flows forward, with past informing present, and past-informed present prefiguring the future. (p. 594)

The appropriateness of any use of the "ladder" metaphor has of course been challenged from some perspectives, most notably by feminists concerned with the patterns of dominance implied by hierarchical metaphors. For example, Alison Bailey (Locating Traitorous Identities: toward a view of privilege-cognizant white character, In: Deborah Orr, et al. Feminist Politics, 2007) uses language that could appropriately inform a richer understanding of a Periodic Table of Life:

Not a climb up the ladder, but a discarding of the hierarchies and rigidities implicit in the ladder metaphor. It involves recognition of the plasticity and the thickness of identities, a new understanding of the ways in which identities interlock, being freed from old limitations, and the emergence of new possibilities....

Magic square ordering? In relation to the Zen pattern, a potential response to the above constraints is the non-linear ordering offered by the simple 3x3 magic square -- of which there is only one (excluding rotations and reflections). Clearly this pattern provides a device for a tenth condition, then associated with the pattern as a whole. The central condition could be similarly excluded to provide a correspondence with the Chinese BaGua mirror pattern of 8 trigrams.

Magic square 3x3

Corresponding ordering of Zen stages?

traces
(problematizing)

transcended
(integrating)

riding
(governing)

source
(believing)

taming
(protecting)

search
(questioning)

catching
(acquiring)

perceiving
(modelling)

both transcended
(conscientizing

Possibly as a consequence of the human cognitive constraint, this simple magic square is indicative of an elusive form of interlocking between the numbers of perspectives characteristic of models variously preferred as "ways of looking", as separately exemplified (Systems of Categories Distinguishing Cultural Biases, 1993).

Whilst the 9+1 are held by the square (as suggested), there are 8 perspectives on it, each totalling to 15 (as indicated). Each of these is composed of three numbers, thereby recalling the distinctive composition of the 8 BaGua trigrams.

Occluded functions: Especially intriguing is the sense in which the pattern might be reduced by neglectful exclusion of particular rows, columns or diagonals. Following Miller, a 10th and 9th order of insight might be "occluded" in a more comprehensive 10-fold pattern.

Bull, ox and/or cow? There is a possibility that any such configuration might be systemically relevant to a juxtaposition of "bull-as-misrepresentation" with "bull-as-disruptive" -- remarkably exemplified in this period by both the reality distortion of Donald Trump (and other leaders) and their justification of disruptive executive orders. They offer examples of the classic "bull in a china shop", whether understood tangibly or intangibly (Charles Duhigg, White House Echoes Tech: 'Move Fast and Break Things', The New York Times, 8 March 2017).

In the following tentative articulation, "ox" is understood as a deliberately imposed constraint, whether cognitive (as a form of reductionism) or physical -- both being consistent with an analogue to castration. Use is made of "cow" as a precursor condition to either the unpredictable wildness of "bull" or to the "ox" (however questionably domesticated or reduced). Alternative "calf" might be used. Both cow and calf have been distinctively valued in cultures of the past.

Configuration as a circle (of eternal return): As a further exemplification of the above argument, the traditional linear sequence of those "ox-herding" images can however be configured in a circle as follows -- as previously explored in the Experimental configuration of nothingness as an "eightfold way" (2012). The magic square might be understood as an approximation to this -- exemplifying other aspects of the connectivity vital to systemic comprehension.

With respect to the above argument for an "eightfold way", it is appropriate to note that the last two images of the sequence relate to cognitive modalities transcending the 8 dynamics. These may be otherwise be held by a configuration of Möbius strips (Experimental configuration of nothingness as an "eightfold way", 2012).These are effectively subsequent to the cognitive modality of the eighth. They might be understood as relating to the two distinct axes of the toroidal form of the "necklace" -- that threading the individual strips together and that associated with its wearer.

The circular configuration of 10 images could then be reconfigured (as below) into an 8-fold pattern with the two additional modalities (or dimensions) represented as overlapping, encompassing or englobing the first in the original sequence. The possible correspondence between the 10-fold pattern and an 8-fold pattern is further highlighted by the existence of references such as the following (The Eight Ox Herding Pictures, 2012; The Eight Ox Herding Pictures: a Chan/Zen allegory).

It has been argued that the original set of the ox-herding pictures ended with the eighth "drawing" -- a blank space, indicating that anything that was depicted above the eighth and final stage would be misleading (How to Practice Zen, 2014). This could be considered to be consistent with arguments for "unsaying", notably as characteristic of apophatic discourse (Michael A. Sells, Mystical Languages of Unsaying, 1994).

Silence on certain matters has traditionally been highly recommended -- even framed as basic to civilized discourse. The core study by Ludwig Wittgenstein (Tractatus Logico-Philosophicus, 1921) concludes with the much-cited phrase: Whereof one cannot speak, thereof one must pass over in silence. The most fundamentally significant experiences of life may indeed be those of which nothing can be said. Nothing that can be said is worth saying?

Suggestive reconfiguration of the above 10-fold circular
ox-herding representation
into the form of an "8-fold way"

Configuration as a torus: In terms of comprehensibility and memorabilty, of interest is the possibility of presenting the above pattern within a torus (as shown below, left). The same approach may be used for any potential correspondence with the BaGua trigram pattern (below right). Such a depiction, especially when animated, evokes other ways of thinking about both in dynamic rather than static terms, as phases in a cycle rather than as stages in a linear progression. The representation is also helpful in suggesting the manner in which the phases may coexist, if only potentially, rather than each being superceded by the next. Any assumption of non-reversibility of time may also be called into question.

Variants of the animation may then enhance imaginative consideration of this possibility, as implied by other variants which could be produced (as noted below).

Animation of simplest torus as container for dynamic cognitive relations

Further implications are suggested by two exploration of mappings of 3x3 patterns in 3D:

As developed by James Grime, inspired by the widely-famed Rubik's Magic Cube (3x3x3), the question is whether the 2D magic square can be fruitfully incorporated into such a form. As extensively described by Katie Steckles (The Maths of the Grime Cube, The Aperiodical, 15 December 2016), the resulting Grime Cube is based upon the so-called perimeter magic square. This is an arrangement of the numbers 1-8 such that the three numbers on each edge sum to the same total (in this case 12). Only six valid perimeter magic squares exist for the numbers 1-8 -- with the consequence that when any two such patterns are overlayed they then sum to 9 as indicated below

Use of a simple dice to hold the pattern of a 3x3 magic square. As discussed by the mathematicians Ie-Bin Lian and Vini Wu (Paradoxes on Chinese Dice and Magic Square, 2003) the equal-sum property of the columns, rows
and diagonals on magic squares are mapped to sets of equal-expectation dice, thereby highlighting the
associated paradoxes. The numbers in each row, column or diagonal of the magic square are assigned as the number of dots on faces on a dice. For a 3 by 3 magic square, an easy way is to s assign each of the three numbers to two faces of a regular dice.

The configuration of 10 and 15 can be most fruitfully held by various mappings in 3-dimensions on the icosahedron (as discussed below). Further insight may be obtain from a discussion of the enneagram in relation to the magic square and the BaGua pattern (Introducing the Celtic Enneagram)

Configuration as polyhedral great circles: The cognitive coherence of any potentially dynamic coexistence of the different conditions of the Zen pattern (or of any 8-fold trigram correspondence)
can be fruitfully explored through polyhedral configurations. This would of course then have implications for any sense of facticity. The icosahedron (or its dodecahedral dual) are especially useful for this purpose. Of particular interest to any such mapping are the groups of associated great circles (as separately described and illustrated) [Ref: 'Geodesic Math And How To Use It, pp. 50-51, fig 7.6-7.8]:

Family I: 6 great circles: Opposing vertices are used for the poles of spin. This creates six great circles which subdivide each face of the spherical icosahedron. This marks on the sphere the spherical equivalent of the icosidodecahedron with 20 spherical triangles and 12 spherical pentagons.

Family II: 15 great circles: Opposing mid-edge points are used for poles of spin -- creating 15 great circles which outline every icosahedral face and slice through each three ways.

Family III: 10 great circles:
Opposing mid-face points are used for poles of spin -- creating 10 great circles; each one leaving the midpoint of a face edge to cross the next face edge at right angles. The circles are normal to the 10 axes of the corresponding dodecahedron. This enables one mapping of the Zen images (as shown below). The circles can be understood as dividing the icosahedral circumsphere into 20 distinct hemispheres; dividing the surface of that sphere into a total of 92 regions: 60 triangles, 20 hexagons, and 12 pentagons (N Points On Sphere all in One Hemisphere, MathPages).

In embodying so explicitly the 10-fold and 15-fold within a coherent framework, the icosahedron (or its dual) presents the challenge of how the relationship between such mappings is to be comprehended. These raise intriguing questions as to the relationship of the 10 to the 15, as previously suggested by the 3x3 magic square -- and to the 8-fold Bagua set. The fundamental implications are suggested by the building block of life, namely the carbon atom:

Potential concurrence of cognitive conditions: The animations below emphasize the manner in which the cognitive conditions distinguished by the Zen pattern may be to some degree co-existent or activated in some complex sequence -- with some only emerging very briefly (as with the half-life of some carbon isotopes). This would contrast with the traditional sense in which the images are associated with a linear cognitive development, typically as a consequence of a lifetime of meditative experience, if at all.

Icosahedron as a container for 10 Zen images mapped onto 10 great circles

Options for image dynamics within the icosahedron -- with cognitive implications

rotate icosahedron as a whole -- vertically or horizontally

change transparency/visibility of images -- at different rates

increase/decrease image diameter -- at different rates

rotate images -- at different rates

colour images distinctively -- at different rates

reverse images (making 10x2 = 20) -- at different rates

combine any of the above (possibly with rhythmic phasing)

The visualization options engender a complex cycle of images suggesting that their greatest value for the viewer might derive from interactively switching between such options according to their appeal, most notably between rapid rates ("busy") and slower rates ("meditative"). It should be emphasized that (in their x3d or wrl versions) changes to the source files can be readily made with a simple text editor.

With regard to any such concurrency, Conrad Pritscher quotes Thomas Merton to the effect that:

Enlightenment is not a matter of trifling with the facticity of ordinary life and spiriting it all away. As the Buddhists say, nirvana is found in the midst of the world around us, and truth is not somewhere else. To be here and now where we are in our "suchness" is to be in nirvana, but unfortunately as long as we have thirst (desire or craving) we falsify our own situation and cannot realize it as nirvana. (Einstein and Zen: learning to learn, 2010, p. 138)

Mapping onto other polyhedra: Given the division of the cricumsphere of an icosahedron into 92 regions (as noted above), it is appropriate to note the possibility of mappings onto a limited group of the Johnson solids (92 strictly convexpolyhedra that have regular faces but are not uniform).

Polyhedra offering a coherent reconciliation of mapping patterns of 8, 9 and 15

The central image is an enneahedron, one of 2606. Seemingly also of great significance to the possibility of any such mapping is the much-studied Herschel graph (with numerous social) and the enneahedron derived from it. That polyhedron has only recently been visualized following the work of Christian Lawson-Perfect (An Enneahedron for Herschel, The Aperiodical, 1 October 2013). As he describes the graph:

It's the smallest non-Hamiltonian polyhedral graph -- you can't draw a path on it that visits each vertex exactly once, but you can make a polyhedron whose vertices and edges correspond with the graph exactly. It's also bipartite -- you can colour the vertices using two colours so that edges only connect vertices of different colours. The graph's automorphism group -- its symmetries -- is D6 -- the symmetry group of the hexagon. That means that there's threefold rotational symmetry, as well as a couple of lines of reflection.

Using the forms of carbon as a potential guideline to psychosocial organization, of particular interest is the alternation of bonding most notable in the benzene molecule fundamental to the structure of organic tissue. This alternation is termed resonance. It is then relevant to think of the possibility that distinctive mappings onto polyhedra, variously highlighting 8, 9, 10 and 15 (for example), may be associated with a dynamic process of "morphing" between such forms. Rather than any singular polyhedron providing privileged comprehension of the phase transitions exemplified by the Zen images, a variety of such polyhedra may be of significance to such comprehension and its communication.

Whilst the circle can indeed be used in the configuration of the Zen pattern as a whole (through the torus), it is curious to note the emphasis placed on the ring in engaging with the bull, and in the process of controlling its wildness and taming it for domestic purposes. What insight is associated with the nose ring of the bull/ox -- especially now that the fashion for body piercing notably includes such a nose ring, widely used in cultures of the past? Significant value of course continues to be attached to the finger ring, necklace, bracelet, or torc. The value may be most implicit in the ritual use of circlets of beads (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000).

Why is a ring so central to epics of recent times, whether Wagner's "ring cycle" (The Ring of the Nibelung) or Tolkien's The Lord of the Rings? Any such ring pattern can be understood as echoing other traditional images, namely that of the Ouroboros or Quetzalcoatl -- the dragon "biting" its tale -- as a symbol of cyclical recurrence, understood cognitively.

Missing feminine? Using the device of the Zen ox-herding pictures curiously highlights -- perhaps most appropriately -- what is not explicitly highlighted or indicated in any way. Whether bull or ox, it is difficult to imagine any more masculine-oriented pattern with its depiction of the male figures in the images, including the encounter in the final picture between the questionably enlarged epitome of wisdom and the diminutive neophyte.

Implied "feminine" complement as container metaphor: Use of the "bull" as the central symbol of the Zen pattern favoured in an Eastern culture recalls the importance attached to bull-related symbolism in early Egyptian culture -- in which the feminine was celebrated, most notably through the cow-goddess Hathor, typically depicted with horns. As noted above, any such implication is conventionally deprected through reference to "sacred cows" -- whether to be understood as evident or unquestionable.

Using a depiction of the mythological complement to Horus, the following animation then suggests a provocative reframing of the cognitive dynamic for the above argument developed through the bull-pattern. The animation (on the left) was previously developed to suggest the "twinkle" in the strategic third eye of sustainability (Embodiment of Identity in Conscious Creativity: challenge of encompassing "con", 2011). The subtitle of that document emphasized the necessary cognitive vigilance to transcend the confidence games -- the "bull" -- so typical of conventional approaches to strategic governance.

Animations using Hathor as
variously suggestive
of a vehicle for transcendent insight exemplifying n0n-duality?

Although any evocation of Hathor may be readily considered extraordinarily inappropriate in this period, it is remarkable to note the value attached to a complex of insights with which it is specifically associated by speculative freemasonry. Given the leadership role attributed to Freemasonry in governance, whether as claimed by Freemasons or suspected by conspiracy theorists, in the current context it is also remarkable to note the significance attached by them to magic squares (Speculation on the symbol of the Square and Compasses: the Freemasons' Magic Square Square, Review of Freemasonry). This is discussed separately, notably with respect to implications of the seemingly missing feminine dimension (Magic square integrity and implications for the US Constitution, 2015).

Eliciting the "pattern that connects" via "bull"?

The argument above addresses the challenge of clarifying subtle distinctions, rendering them memorable, and configuring them usefully. There is however the fundamental issue of the transitions between such distinctions, the pathways these may imply, and their complementarity under a variety of conditions.

Of interest, however, are the implications of "muck" -- understood here as "bull" -- for the next cognitive revolution and paradigm shift. It could well be that the challenge "lies" in the "bull" in which one believes (if not a "sacred cow") -- especially including a belief in nothing (Emerging Significance of Nothing, 2012). There is a sense in which if one does not understand how one is part of the problem, one cannot understand the nature of the solution required. There is then good cause for epistemological panic (Epistemological Panic in the face of Nonduality: Does nothing matter? 2010).

"Magic" squares? As commonly framed, there is no lack of "bull" in the argument above, especially through the manner in which it touches on symbolism and numerology. This is highlighted in the case of "magic squares", despite the considerable importance associated with them from a mathematical perspective, most notably with respect to number theory. Thus for Ezra Brown (Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves, College Mathematics Journal / Mathematical Association of America, September 2001):

I came across a little gem of a result that ties many mathematical threads together, threads that originate in several different areas of mathematics. The result is that every elliptic curve has nine points of inflection which can be arranged, in a very natural way, to form a 3 x 3 magic square.

Can mathematicians be accused of indulging in deliberate obscurantism, as is evident from answers to questions raised in various fora (How do I study and conduct research in the areas of elliptic curves and modular forms? Quora, 2014; What is so special about elliptic curves?Physics Forums, 2013). Self-reflexively, are elliptic curves themselves relevant to the challenge of comprehension, in the light of some responses offered: Elliptic curves are interesting because they are the simplest algebraic structure that is not yet completely understood; The problem I fear is that's it's not going to be easy to understand if we're not already familiar with the subject.

Given the early slogan of the industrial revolution, what indeed is the "manure" from which "brass" can be derived? Appropriately "brass" was then a reference to money -- and is therefore relevant to the fundamental issues of confidence which are now proving so critical with respect to facticity.

Connectivity: enneagram vs magic square: If the issue is one of comprehensible connectivity, one exercise deriving from the above argument is to confront the connectivity of the enneagram with that of the magic square.

Enneagram

Enneagram rotated

3x3 Magic square

Numbers in corresponding positions in the enneagram sum to 7, 8, 9, 10 or 11, as indicated in the image on the left (below). If the corresponding numbers in the columns, rows or diagonals from the magic square are summed, they give the totals 9, 10, and 12, as indicated in the image on the right -- based on their relative positions in the enneagram. The areas in that diagram are then necessarily indicative of the 15 to which the three numbers total in each case (as a property of the magic square indicated above). Note that these results would have been visually identical had the enneagram been rotated in the other direction.

Such patterns are indicative of the connectivity within which the transitions between the Zen insight phases could be understood to be embedded. Especially intriguing as an indication of comprehensibility are the various symmetries in the image on the right (above) which are more apparent in the images which follow.

Points of inflection and a 3x3 magic square: The above-mentioned exploration of magic squares by Ezra Brown suggests an unexpected convergence of threads relevant to this argument. He frames a Magic Square Theorem:

Every elliptic curve has nine points of inflection, and these points form an affine plane of order 3. That is, each point of inflection lies on exactly four lines, each of which contains two other points of inflection -- making 12 lines in all -- and each pair of points of inflection determines a unique line (Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves, 2001)

Five "plus or minus four"? Noting the resemblance to the argument of Viktor Prasolov and Yuri Solvyev (Elliptic Functions and Elliptic Integrals, American Mathematical Society, 1997), Ezra Brown concludes by showing how the 9 inflection points can be arranged as a 3x3 magic square (left half of table below). He argues that this result ties together threads from finite geometry, recreational mathematics,
combinatorics, calculus, algebra, and number theory.

Memorability: foldability and degeneracy? With respect to learning or insight, why 5 rather than 7 ? Intuitively interrelation of 5 points is already a challenge, as with comprehension of the subtleties of orders of feedback and self-reference greater than 3 -- with 5 at the limit of current cybernetic considerations. The sense in which 5-fold comprehension "decays" to 5-1, 5-2, 5-3 or 5-4 comprehension can be readily recognized, with dysfunctional polarization the most common of psychosocial processes, and with the concerns regarding the unitary assertion of fact being the focus of the above argument. Potentially relevant is the coherence associated with the five points determining a conic in projective geometry.

... folding suggests an interlacing of thought and contemplation together with a materialized geometry and partially overlapping events. This enables Fuller to tie together his conception of geometry as a material mathematical science -- a point is a place where two lines pass through but not at the same time -- and the scenario as a form of thinking. Folding, weaving and interlacing engender this form of thinking.

To what extent might "foldability" be relevant to the coherent organization of memory with respect to different levels of complexity?

Given the above-cited approach of Lakoff and Nuñez (2011), it might also be asked whether the frequent use by mathematicians of "embedding" is indicative of the poorly extent to which human subjective experience is embedded in the objective reality of mathematics -- matched by the extent to which the latter "informs" subjective experience.

Points of inflection in the learning process? Curiously the literature focuses on the challenge of learning about the importance of elliptic curves but not on their implication for the learning process itself -- with the exception of some hints to that effect (Apostolos K. Doxiades and Barry Mazur, Circles Disturbed: the interplay of mathematics and narrative, 2012; Roberto Festa, et al. Cognitive Structures in Scientific Inquiry, 2005). The symmetries of the image on the right above are however suggestive of correspondences in the comprehension of 4 (=5-1) and 6 (=5+2), as well as of 3 (=5-2) and 8 (=5+3), for example.

The relationship established by Brown to elliptic curves is valuable because the kind of learning associated with the Zen pattern of distinctions is essentially non-linear and usefully understood in terms of elliptic curves and points of inflection -- from concave to convex -- potentially to be considered in terms of the insideness (subjectivity) or outsideness (objectivity) of perspective (Transformation of worldview from "inside-outside" to "outside-inside", 2013).

Stabilizing facticity: encycling the serpent and the snake lemma: The points of inflection are explained otherwise in Wikipedia by use of the following animation (on the left) with its suggestively snake-like dynamic.

From Wikipedia, produced by Thomas Cooper; created with a GNU Octave script; Public Domain, Link

Zen image #8

Screen shots of animation
by Michael Verderese

The serpentine movement of the animation ironically suggests -- however naively -- that it is indeed snakes that have the most instinctive understanding of an "elliptic dynamic" which they embody in their movement. The challenge of self-reflexive learning might then be usefully framed by the snake "biting its tail", as with the Ouroboros symbol on the right above -- echoed by one of the images in the Zen pattern. The tail-biting image is also renowned for the insight it offered into the discovery of the structure of the benzene molecule fundamental to biological tissue, as illustrated in the screen shots above from an animation by Michael Verderese (An HTML-based Representation of Kekulé's Benzene Dream, ChemDoodle, 2011), and variously discussed (Malcolm W. Browne, The Benzene Ring: dream analysis, The New York Times, 16 August 1988).

Encycling a paradoxical snake in a Möbius strip: As widely noted, an elliptic curve is a challenge to comprehension. Elliptic curves are of the following topological types: a torus, an annulus, a Möbius strip, and a Klein bottle (North-Holland Mathematics Studies, 54, 1981). A Möbius strip is a challenge to comprehension in mathematical terms -- although easy to visualize through constructing one (Understanding the Equation of a Möbius Strip, Mathematics Stock Exchange, 2014). Any challenge to learning, with the requisite "cognitive twist" of a paradigm shift, might then be understood as usefully embodied into a Möbius strip in some way -- beyond the relatively simplicity of framing the Zen pattern within a torus (as indicated above).

"Re-cognition" of the nature of the challenge is usefully indicated by the manner in which depiction of wisdom in iconography may use some form of halo or annulus, even taking the form of a torus. Such depiction may include use of the infinity symbol, readily implying the paradoxical complexity of a Möbius strip. The cognitive peculiarity of the relationship between "global experience", the "toroidal journey" of eternal return, and the "paradoxical twist" linking alternative world views can be explored in terms of the corpus callosum nexus of the human brain (Corpus Callosum of the Global Brain? 2014; Engendering Viable Global Futures through Hemispheric Integration, 2014). Any dynamic integration of "facts" and modalities, as implied by the Zen "herding" metaphor, can then be contrasted with the implication of "herding cats".

Better still would be to explore any way of combining a torus mapping with that of a Möbius strip. One approach is suggested by a double twisted Möbius strip fitted into the form of a torus; otherwise known as a bifilar torus knot, this is discussed and depicted separately (Möbius and Torus Relationship, The Life Field Transformer).

Experimental association of Möbius strip with torus

Test error A

Test error B

Animation of progression

Presentation of the test errors above recalls the range of topological distortions of the Möbius strip through introduction of extra twists -- with their potential cognitive implications.

Here, we show that DNA origami can be used to assemble a Möbius strip, a topological ribbon-like structure that has only one side. In addition, we show that the DNA Möbius strip can be reconfigured through strand displacement to create topological objects such as supercoiled ring and catenane structures.

Verbal explanation of any "twist" is essentially unhelpful to forms of comprehension dependent on linearity. The following images and animations can therefore be understood as experiments in the facilitation of comprehension implying "paradigm twists". The challenges to their construction using 3D visualization facilities are also significant in that respect -- notably through the failures to engender results which combine both comprehensibility and appeal. The question is on what forms can new insight be meaningfully "hung" -- and in what forms can it be fruitfully embodied (In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007).

Torus knotting and helicoidal animation:Mnemonic clues to to the nature of the cognitive challenge may also be offered by topological complexification of the basic torus as suggested below -- and as previously developed (Configuration of a Toroidal Helix, 2016).

Potential use of a continuous toroidal knot with 9 windings
as a container for the Zen or BaGua pattern(Interactive variants: X3D or VRML)

Options for disk dynamics -- with cognitive implications

disk movement along Möbius strip

disk movement through knot

Rather than the Zen images, the contrasting subtleties of 9 insight modalities can be encoded by colour, as shown below. The representation can be readily varied by modifying parameters of: colour, cycle period, ball size, number of balls, period of visibility, radius of helicoidal winding. Any given combination of choices may well range from appealing to alienating -- and meaningless. This suggests that such an animation is best explored like an interactive musical instrument on which a variety of "cognitive melodies" can be explored (possibly enhanced with associated tonal encoding typical of sonification). Those recognized as appealing are then evocative of more integrative insight. Those which are variously alienating are then suggestive of possible cognitive traps. Such an instrument lends itself to depiction of both habitual modes of busyness and occasional flashes of insight.

Animation in 3D of movement of 9 balls around a continuous toroidal knot
(.x3d source)

A related design metaphor that can be used as a suggestive container for the dynamics of the Zen pattern is indicated below. There the images circulate through a hierarchical winding. Again a wide variety of dynamics can be associated with the images as an aid to "re-cognition". As noted earlier, a tenth image could be associated in some way with the pattern as a whole (perhaps as suggested by that on the right). The pattern could be rendered in an 8-fold form using the distinctions of the BaGua trigrams (as above).

Correspondence with the coaction cardioid? There is a further possibility that the learning process associated with the pattern of the magic square could be fruitfully explored in the light of the work on the coaction cardioid, within a similar pattern, by Edward Haskell (Full Circle: The Moral Force of Unified Science, 1972), and further developed by Timothy Wilken (UnCommon Science, 2001) into the following generic form:

Reality and unreality? With respect to any sense of "reality", Brown shows that only two of the nine points of inflection on an elliptic curve are defined by real coordinates, the others have at least one nonreal coordinate -- meaning that they cannot be readily seen. An insight of this kind would seem to merit careful consideration in terms of the subtlety of the learning process indicated by the Zen pattern. This "unreality" is seemingly acceptable to science -- perhaps as "good shit" in the widely circulated schema of such perspectives (Shit Happens: close-to-complete ideology and religion shit list).

Of potential relevance is the relation of such curves to the work of René Thom, basic to catastrophe theory -- with learning readily understood as a succession of cognitive catastrophes (Structural Stability and Morphogenesis: an outline of a general theory of models, 1972; Esquisse d'une Sémiophysique: physique aristotélicienne et théorie des catastrophes, 1989).

Especially intriguing with respect to the above argument is the manner in which deep learning has been defined (Deep Learning in 7 lines of code (Chatbot's Life, 7 April 2017). The latter emphasizes that the essence of machine learning is recognizing patterns within data. This is achieved by use of layers of abstraction, otherwise known as "frameworks" -- a term subject to confusion (Enrico Busto, Deep Learning Frameworks Explained, Add-for, 2 November 2016). It is curious that highlighting 7 such layers is consistent with the cognitive constraints highlighted above: "plus or minus 7". More curious is the degree to which the layers of abstraction bear comparison with the Zen images as indicative of progressive abstraction -- especially as frameworks for cognition. The emphasis on "7 lines of code" also suggests a charmingly reminiscent comparison with the poetic lines by which the cognitive significance of each ox-herding image is indicated.

Layers of abstraction: Less obvious is whether 7 abstraction layers is deemed sufficient for deep learning or a necessary prerequisite. The ISO-OSI networking model comprises seven such layers. Each layer encapsulates and addresses a different part of the needs of much digital communication, thereby reducing the complexity of the associated engineering solutions. With respect to the argument above for "5 plus or minus 4", one exception appears to be the use of 9 such layers, usefully articulated for GIS (Stuart Hodgson, et al. Geographical Information '97: From Research to Application Through Cooperation, 1997, volume 2, p. 290-1):

Five of these model the abstraction from real world to project world and the interfaces between them: The essence of the real world is captured in the name's and descriptions of thc conceptual world; the conceptual world is modeled on the simplified or generalized constructs of geomatics in the geospatial world; the geospatial world is more rigorously defined in the metrics and spatial objects of the dimensional world; and finally the dimensional world is codified in the project world of a particular domain, along with its definitions of space, vocabulary, methods or observation. and classifications of entities and phenomena.

The remaining four abstractions define in increasing detail the mechanism of encoding thc elements of thc project world in terms of thc data and services model of Open GIS. In order, these are: thc points world of coordinate geometry; the geometry world of well-known geodata types; the feature world which combines spatial and non-spatial attributes of geographic objects according to schemas of properties and their values; and the feature collection world which provides an overall structure and taxonomy to all of the elements in the underlying project world.

Out-smarting the other: Clearly the interest for Google lies in the competitive advantage to be derived from more sophisticated approaches to the data it holds in various forms. It is for this reason that much has been made of the development of these techniques (through DeepMind, a Google-owned company) to winning board games against their grand masters, most notably through the AlphaGo application (Dom Galeon, Google's AI Is Changing the Way a 3,000-Year-Old Game Is Played, Futurism, 9 April 2017). The Future of Go Summit (May 2017) is a collaboration between the Chinese Go Association, the Chinese government, and Google. Leading AI experts from both Google and China will be in attendance with the aim of testing AlphaGo's creativity and adaptability, plus its ability to work in tandem with human players.

Of particular relevance to the argument above is the underlying assumption that "deep learning" is now intimately related to an unchallenged primary preoccupation with a form of "winning" whose nature is not open to exploration. This is exemplified in strategic board games, such as chess and go, in which the objective is to determine a single "winner" (through effectively "breaking the spirit" of a "loser"). Hence the military and corporate interest in such applications as a means of "out-smarting" any opponent. The implied "depth" of the learning seemingly does not go beyond the desirability of that binary outcome.

Bullying the other: Ironically, given the framing of the above argument, go terminology includes the term ijime -- translated as "bullying" -- referring to the freedom of sente moves offered by playing against weak positions. In the light of the Zen pattern of distinctions, the preoccupation of "winning" in this manner -- and the freedom to "bully" an opponent -- corresponds to no more than a middle phase in the learning process. The distinctions made in that respect are Catching the "bull", prior to Taming the "bull", prior to Riding the "bull" home (with the latter caricatured by a self-satisfied Don Quixote).

Should such board games be seen as exemplifying the vicarious pleasure from determining who can "bully" the other "better" -- in anticipation of their total "annihilation"? Is such the perversity underlying much competitive game playing?

There is no "re-cognition" of the subtler distinctions: The "bull" transcended, Both "bull" and self transcended, or Reaching the source of the "bull" -- but especially any sense of Return to society (rather than its exploitation by any "winner"). The problematic facticity of marketing "bull" is of course to be expected with respect to the latter. There is no implication that insights from deep learning will in any way contribute to reframing violent binary conflict -- as currently exemplified by Israel/Palestine, Christianity/Islam, and USA/Russia. Arguably there is no evident motivation to develop learning in this way.

The irony is all the greater in that radical Islam has been surprisingly successful strategically through "re-cognizing" the modality of personal sacrifice. Despite expenditure of trillions of dollars over decades, exploiting every form of global "intelligence", no insights have emerged regarding how to contain this paradoxical individual commitment. The focus of intelligence has been limited to threat identification, targetting and hacking -- and the avoidance of personal sacrifice (except that of others). There is no sense that artificial intelligence encompasses the existential sacrifice of the player -- rather than one of it pawns.

Reality bubble collapse and emergence of self-reflexivity: In a period in which the risk of nuclear conflict is considered imminent, the pattern of Zen images can be interpreted as embodying the transition between the collapse of the reality bubble of an inadequate paradigm and the emergence of a higher order of self-reflexivity.

Recognition of subtler patterns: Given the emphasis in AI on recognition of ever subtler patterns, this necessarily recalls both the cybernetic levels of self-reflexivity (noted above) and the pattern language preoccupation of Christian Alexander. Of particular relevance is his focus on what he names as "a quality without a name" and a "place to be":

There is a central quality which is the root criterion of life and spirit in a man, a town, a building, or a wilderness. This quality is objective, but it cannot be named... every place is given its character by certain patterns of events that happen there. These patterns are always interlocked with certain geometric patterns in the space... To reach the quality without a name we must then build a living pattern language as a gate. (A Timeless Way of Building, 1979, pp ix-xi)

From a strategic perspective, also curious is how AI's layers of abstraction may make use of deception, or embody it, given its fundamental importance to any intelligent martial endeavour. As "bull", such deception is presumably to be considered a quintessential form of "fake news" -- which Google now claims to be removing from its search results through new algorithms. If quantitative easing (through fiat money) has proven to be so vital to economic sustainability, might "printing facts" not have an analogous role? Is "faking it" an essential feature of any viable form of intercourse?

Intimacy vs Abstraction: calling hierarchy into question: As noted above with respect to what is "missing", the language of "levels" of cognitive abstraction is of course subject to criticism. It necessarily implies patterns of male dominance -- of concern from a complementary feminine perspective. Missing is the sense in which subtler cognitive insight may imply greater degrees of "cognitive intimacy" in relation to any sense of otherness. Rather than the detachment formalized by abstraction, this is readily experienced as fundamentally boring in contrast with experiential reality.

This could be understood as exemplified through the sequence of images of a bull by Pablo Picasso (Bull: a Master class in Abstraction) and their implications for his abstraction of the feminine through Cubism. As a consequence of being the subject of such "abstraction" -- as with eunuchs and castrati -- do oxen dream of having balls and a functional erection? As separately discussed, it is tragically appropriate in symbolic terms that the person hailed as the innovator of computer advances on which AI is now based should himself have been literally castrated by convention at the peak of his creativity (Imagining Order as Hypercomputing Operating: an information engine through meta-analogy, 2014).

The nature of any subject-object duality is called into question through deep learning understood otherwise. This may imply increasing degrees of cognitive embodiment of "reality" in contrast with patterns of abstraction from it -- although the two may well come to be conflated in some way.

As noted above, the ambiguity of "bull" in the Zen phases is succinctly indicative of the self-referential process of engaging with an emergent pattern of abstraction of greater subtlety -- both in terms of of its intractable dynamic and its deprecation as a delusion or conceit from any more conventional perspective.

Recursive embedding? The current deployment of resources with respect to the go board game offers a further irony in relation to the above argument. Go is played on a 19x19 board, apparently offering far greater complexity than the 3x3 magic square with respect to which the Zen distinctions were made. However the strategic challenges of the game may well be determined in a 3x3 context within the board -- as evidenced by the Knight's move of chess (indicated above) and notions of shape in go.

Rather than the current focus on the Turing Test in relation to artificial intelligence, is the need for some form of "Tesla Test" to distinguish forms of deep learning of psychosocial significance transcending duality?

There is however the ironic possibility that humans might themselves be unable to "re-cognize" any such creative paradigm shift (Engaging with Insight of a Higher Order, 2014; Eliciting a Universe of Meaning -- within a global information society of fragmenting knowledge and relationships, 2013). The point is provocatively highlighted by the manner in which cognitive "levels" of pattern recognition are associated to some degree with age -- in a global society characterized by variously increasing proportions of the young and the old. What is AI to do when the data at its disposal embodies the "wisdom of the ages" -- at the subtlest levels of abstraction -- but must respond to the binary preferences of the young? Is deceptive dumbing down then a necessity -- as traditionally embodied in riddles? Is that how the Zen of facticity is to "re-cognized"?

Claudio Masolo. Understanding Ontological Levels. Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning (Association for the Advancement of Artificial Intelligence), 2010, pp. 258-268 [text]